Ghost cuts of the nucleon propagator

We demonstrate in our work, on the special example of dressing the nucleon propagator, that if ghost poles exist, they lead to ghost cuts, and the ghost cuts generate new ghost cuts. The geometry of the location of these cuts in the complex s plane is fully discussed and analyzed. We found a simple exact parametric representation of the nth ghost cut: s=sg(1-p)+(nμ)2p, where p is a real parameter 0≤p≤1, sg is the location of the ghost pole, and μ is the pion mass. When the location of the ghost pole approaches the nucleon pole, the ghost cuts approach the unitarity cut. The renormalization procedure is adopted to the case of a ghost pole appearing on the real axis of s.